{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2023,11,15]],"date-time":"2023-11-15T11:44:40Z","timestamp":1700048680081},"reference-count":48,"publisher":"Wiley","issue":"1","license":[{"start":{"date-parts":[[2004,1,8]],"date-time":"2004-01-08T00:00:00Z","timestamp":1073520000000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Mathematische Nachrichten"],"published-print":{"date-parts":[[2004,2]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>We consider the Dirichlet problem for the stationary Navier\u2010Stokes system in a plane domain \u03a9, with two angular outlets to infinity. It is known that, under appropriate decay and smallness assumptions, this problem admits solutions with main asymptotic terms in Jeffrey\u2010Hamel form. We will approach these solutions by constructing an approximating problem in the domain \u03a9<jats:sub><jats:italic>R<\/jats:italic><\/jats:sub>, which is the intersection of \u03a9 with a sufficiently large circle. The main difficulty, in contrast to the corresponding linear problem, arises from the fact that the main asymptotic term is not known explicitly. Here, we create nonlinear, but local, artificial boundary conditions which involve second order differential operators on the truncation arcs. Unlike for the analogous three\u2010dimensional exterior problem, we are able to show the existence of weak solutions to the approximating problem without smoothness nor smallness assumptions. For small data, we prove that the solutions of the approximating problem are unique and regular. Finally, we reach the main goal of this work, i.e. we obtain error estimates in weighted H\u00f6lder spaces which are asymptotically precise as <jats:italic>R<\/jats:italic> tends to infinity. (\u00a9 2004 WILEY\u2010VCH Verlag GmbH &amp; Co. KGaA, Weinheim)<\/jats:p>","DOI":"10.1002\/mana.200310135","type":"journal-article","created":{"date-parts":[[2004,1,9]],"date-time":"2004-01-09T08:01:47Z","timestamp":1073635307000},"page":"24-67","source":"Crossref","is-referenced-by-count":4,"title":["Nonlinear artificial boundary conditions for the Navier\u2010Stokes equations in an aperture domain"],"prefix":"10.1002","volume":"265","author":[{"given":"Sergue\u00ef A.","family":"Nazarov","sequence":"first","affiliation":[]},{"given":"Maria","family":"Specovius\u2010Neugebauer","sequence":"additional","affiliation":[]},{"given":"Juha H.","family":"Videman","sequence":"additional","affiliation":[]}],"member":"311","published-online":{"date-parts":[[2004,1,8]]},"reference":[{"key":"e_1_2_1_2_2","unstructured":"R. A.Adams Sobolev Spaces (Academic Press New York 1975)."},{"key":"e_1_2_1_3_2","doi-asserted-by":"publisher","DOI":"10.1007\/BF00381276"},{"key":"e_1_2_1_4_2","doi-asserted-by":"publisher","DOI":"10.14492\/hokmj\/1381517172"},{"key":"e_1_2_1_5_2","doi-asserted-by":"publisher","DOI":"10.1016\/S0021-7824(97)89944-8"},{"key":"e_1_2_1_6_2","doi-asserted-by":"publisher","DOI":"10.1002\/(SICI)1099-1476(199702)20:3<245::AID-MMA856>3.0.CO;2-F"},{"key":"e_1_2_1_7_2","doi-asserted-by":"crossref","unstructured":"G. P.Galdi An Introduction to the Mathematical Theory of the Navier\u2010Stokes Equations. Vol. II. Nonlinear Steady Problems Springer Tracts in Natural Philosophy Vol. 39 (Springer\u2010Verlag New York 1994).","DOI":"10.1007\/978-1-4757-3866-7"},{"key":"e_1_2_1_8_2","doi-asserted-by":"publisher","DOI":"10.1512\/iumj.1996.45.1157"},{"key":"e_1_2_1_9_2","doi-asserted-by":"crossref","unstructured":"I. C.Gohberg andM. G.Krein Introduction to the Theory of Linear Nonselfadjoint Operators (Amer. Math. Soc. 1969).","DOI":"10.1090\/mmono\/018"},{"key":"e_1_2_1_10_2","doi-asserted-by":"publisher","DOI":"10.2307\/2007649"},{"key":"e_1_2_1_11_2","doi-asserted-by":"publisher","DOI":"10.1137\/0730008"},{"key":"e_1_2_1_12_2","doi-asserted-by":"publisher","DOI":"10.1137\/0520021"},{"key":"e_1_2_1_13_2","doi-asserted-by":"publisher","DOI":"10.1007\/BF02392043"},{"key":"e_1_2_1_14_2","doi-asserted-by":"crossref","unstructured":"J.Heywood Open problems in the theory of the Navier\u2010Stokes equations for viscous incompressible flow in: The Navier\u2010Stokes Equations Theory and Numerical Methods edited by Heywood et al. Lecture Notes in Mathematics Vol. 1431 (Springer\u2010Verlag Berlin 1990) pp. 1\u201322.","DOI":"10.1007\/BFb0086051"},{"key":"e_1_2_1_15_2","first-page":"151","article-title":"Spectral problems in singular perturbed domains and selfadjoint extensions of differential operators","volume":"6","author":"Kamotski I. V.","year":"1998","journal-title":"Trudy St. Petersburg Mat. Obshch."},{"key":"e_1_2_1_16_2","unstructured":"T.Kato Perturbation Theory for Linear Operators 2nded. (Springer\u2010Verlag 1980)."},{"key":"e_1_2_1_17_2","first-page":"209","article-title":"Boundary value problems for elliptic equations in domains with conical or corner points","volume":"16","author":"Kondratjev V. A.","year":"1967","journal-title":"Trudy Moskov. Mat. Obshch."},{"key":"e_1_2_1_18_2","doi-asserted-by":"crossref","unstructured":"V. A.Kozlov V. G.Maz'ya andJ.Rossmann Spectral Problems associated with Corner Singularities of Solutions to Elliptic Equations Mathematical Surveys and Monographs Vol. 85 (Amer. Math. Soc. Providence RI 2001).","DOI":"10.1090\/surv\/085"},{"key":"e_1_2_1_19_2","unstructured":"O.Ladyzhenskaya The Mathematical Theory of Viscous Incompressible Flow (Gordon and Breach New York 1969)."},{"key":"e_1_2_1_20_2","unstructured":"L. D.Landau andE. M.Lifschitz M\u00e9chanique des Fluides (Mir Moscow 1971)."},{"issue":"12","key":"e_1_2_1_21_2","first-page":"1","article-title":"Etude de diverses \u00e9quations int\u00e9grales non lin\u00e9aires et de quelques probl\u00e8mes que pose l'hydrodynamique","author":"Leray J.","year":"1933","journal-title":"J. Math. Pures Appl."},{"key":"e_1_2_1_22_2","unstructured":"J. L.Lions andE.Magenes Nonhomogeneous Boundary Value Problems and Applications. Vol. I Die Grundlehren der Mathematischen Wissenschaften 181 (Springer\u2010Verlag Berlin 1972)."},{"key":"e_1_2_1_23_2","doi-asserted-by":"publisher","DOI":"10.1002\/mana.19770760103"},{"key":"e_1_2_1_24_2","doi-asserted-by":"publisher","DOI":"10.1002\/mana.19780810103"},{"key":"e_1_2_1_25_2","doi-asserted-by":"crossref","unstructured":"V. G.Maz'ya S. A.Nazarov andB. A.Plamenevskii Asymptotics of solutions to elliptic boundary\u2010value problems under a singular perturbation of the domain Tbilisi University (1981). German Transl.: Asymptotische Theorie Elliptischer Randwertaufgaben in Singul\u00e4r Gest\u00f6rten Gebieten Bd. 1 (Akademie Verlag Berlin 1991). English Transl.: Asymptotic Theory of Elliptic Boundary\u2010Value Problems in Singularly Perturbed Domains Vol. I (Birkh\u00e4user Basel 2000).","DOI":"10.1007\/978-3-0348-8434-1_4"},{"key":"e_1_2_1_26_2","first-page":"72","article-title":"On the asymptotic behavior of solutions of elliptic boundary value problems with irregular perturbations of the domain","volume":"8","author":"Maz'ya V. G.","year":"1981","journal-title":"Probl. Mat. Anal."},{"key":"e_1_2_1_27_2","first-page":"699","article-title":"On the two\u2013dimensional aperture problem for Navier\u2013Stokes equations","volume":"323","author":"Nazarov S. A.","year":"1996","journal-title":"C. R. Acad. Sci. Paris, Ser. 1"},{"key":"e_1_2_1_28_2","first-page":"112","article-title":"Asymptotic conditions at points, selfadjoint extensions of operators and the method of matched asymptotic expansions","volume":"5","author":"Nazarov S. A.","year":"1996","journal-title":"Trudy St.\u2010Petersburg Mat. Obshch."},{"key":"e_1_2_1_29_2","first-page":"44","article-title":"The operator of a boundary\u2010value problem with Chaplygin\u2010Zhukovskii\u2010Kutta type conditions on an edge of the boundary has the Fredholm property","volume":"31","author":"Nazarov S. A.","year":"1997","journal-title":"Funkt. Analiz i Ego Prilozheniga"},{"key":"e_1_2_1_30_2","first-page":"207","article-title":"The Navier\u2010Stokes problem in a two\u2010dimensional domain with angular outlets to infinity","volume":"257","author":"Nazarov S. A.","year":"1999","journal-title":"Zapiski Nauchn. Seminar POMI"},{"key":"e_1_2_1_31_2","doi-asserted-by":"crossref","unstructured":"S. A.Nazarov Weighted spaces with detached asymptotics in application to the Navier\u2010Stokes equations in: Advances in Mathematical Fluid Mechanics edited by Malek et al. (Springer\u2010Verlag 2000) pp. 159\u2013191.","DOI":"10.1007\/978-3-642-57308-8_5"},{"key":"e_1_2_1_32_2","first-page":"475","article-title":"On steady Stokes and Navier\u2013Stokes problems with zero velocity at infinity in a three\u2013dimensional exterior domain","volume":"40","author":"Nazarov S. A.","year":"2000","journal-title":"J. Math. Kyoto Univ."},{"key":"e_1_2_1_33_2","doi-asserted-by":"crossref","unstructured":"S. A.Nazarov andB. A.Plamenevskii Elliptic Problems in Domains with Piecewise Smooth Boundaries (Walter de Gruyter and Co Berlin 1994).","DOI":"10.1515\/9783110848915"},{"key":"e_1_2_1_34_2","doi-asserted-by":"publisher","DOI":"10.2140\/pjm.2002.203.461"},{"key":"e_1_2_1_35_2","doi-asserted-by":"publisher","DOI":"10.1016\/S0021-7824(01)01231-4"},{"key":"e_1_2_1_36_2","doi-asserted-by":"publisher","DOI":"10.1016\/S0021-7824(01)01232-6"},{"key":"e_1_2_1_37_2","doi-asserted-by":"publisher","DOI":"10.1524\/anly.1996.16.4.305"},{"key":"e_1_2_1_38_2","first-page":"229","article-title":"Approximation of unbounded domains by bounded ones. Boundary value problems for the Lam\u00e9\u2010Operator","volume":"8","author":"Nazarov S. A.","year":"1996","journal-title":"Algebra i Analiz"},{"key":"e_1_2_1_39_2","doi-asserted-by":"crossref","first-page":"223","DOI":"10.3233\/ASY-1997-14302","article-title":"Approximation of exterior boundary value problems for the Stokes system","volume":"14","author":"Nazarov S. A.","year":"1997","journal-title":"Asymptotic Anal."},{"key":"e_1_2_1_40_2","first-page":"317","article-title":"Artificial boundary conditions for elliptic systems in domains with conical outlets to infinity","volume":"377","author":"Nazarov S. A.","year":"2001","journal-title":"Dokl. Akad. Nauk."},{"key":"e_1_2_1_41_2","doi-asserted-by":"publisher","DOI":"10.1002\/mana.200310039"},{"key":"e_1_2_1_42_2","doi-asserted-by":"publisher","DOI":"10.2206\/kyushujm.53.369"},{"key":"e_1_2_1_43_2","unstructured":"V. Z.Parton andP. I.Perlin Mathematical methods of the theory of elasticity (Mir Moscow 1984)."},{"key":"e_1_2_1_44_2","first-page":"137","article-title":"On spaces of solenoidal vectors","volume":"159","author":"Pileckas K.","year":"1983","journal-title":"Trudy Mat. Inst. Steklov"},{"key":"e_1_2_1_45_2","doi-asserted-by":"publisher","DOI":"10.1137\/0732063"},{"key":"e_1_2_1_46_2","doi-asserted-by":"publisher","DOI":"10.1002\/mma.1670050124"},{"key":"e_1_2_1_47_2","doi-asserted-by":"crossref","unstructured":"H.Sohr The Navier\u2013Stokes Equations (Birkh\u00e4user Verlag Basel 2002).","DOI":"10.1007\/978-3-0348-8255-2"},{"key":"e_1_2_1_48_2","unstructured":"V. A.Solonnikov On the Stokes equations in domains with nonsmooth boundaries and on viscous incompressible flow with a free surface in: Nonlinear Partial Differential Equations and their Applications Coll\u00e8ge de France SeminarsIII Paris 1980\/1981 (Pitman Boston 1982) pp. 340\u2013423."},{"key":"e_1_2_1_49_2","doi-asserted-by":"crossref","first-page":"526","DOI":"10.1115\/1.4010553","article-title":"Stress singularities resulting from various boundary conditions in angular corners of plates in extensions","volume":"19","author":"Williams M. L.","year":"1952","journal-title":"J. Appl. Mech."}],"container-title":["Mathematische Nachrichten"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.wiley.com\/onlinelibrary\/tdm\/v1\/articles\/10.1002%2Fmana.200310135","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/api.wiley.com\/onlinelibrary\/tdm\/v1\/articles\/10.1002%2Fmana.200310135","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/mana.200310135","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,10,18]],"date-time":"2023-10-18T22:41:23Z","timestamp":1697668883000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1002\/mana.200310135"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2004,1,8]]},"references-count":48,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2004,2]]}},"alternative-id":["10.1002\/mana.200310135"],"URL":"https:\/\/doi.org\/10.1002\/mana.200310135","archive":["Portico"],"relation":{},"ISSN":["0025-584X","1522-2616"],"issn-type":[{"value":"0025-584X","type":"print"},{"value":"1522-2616","type":"electronic"}],"subject":[],"published":{"date-parts":[[2004,1,8]]}}}